Augmenting Granger Causality through continuous ordinal patterns

We here propose a novel methodology, based on the concept of continuous ordinal patterns, to preprocess time series and make explicit the non-linear temporal structures in them present. Through a series of synthetic and real-world examples, we show how such transformation overcomes one major limitation of the celebrated Granger Causality test, and allows to efficiently detect non-linear causality relations without the need of a priori assumptions. We further show how such transformation can be optimised based on the time series under study; but that good results can also be achieved using random ordinal patterns, in a way similar to how randomness is exploited in Reservoir Computing. We finally discuss the complementarity between this approach and the standard Granger one, especially in the analysis of real-world, and hence unknown, causal relations.